Prove that vmatrix + + + & ( + )+ ( + ) 2( + )( + ) & + vmatrix = 0

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Prove that ∣α+β+γ+δαβ(γ+δ)+γδ(α+β)2(α+β)(γ+δ)αβ+γδ∣=0\begin{vmatrix} \alpha+\beta+\gamma+\delta & \alpha\beta(\gamma+\delta)+\gamma\delta(\alpha+\beta) \\ 2(\alpha+\beta)(\gamma+\delta) & \alpha\beta+\gamma\delta \end{vmatrix} = 0

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